I'd really like people to expound on why certain items need to be chosen--we're talking to newbies here: what we may see as practical won't be seen as such without saying why.
Okay, I'll bite.
I usually embark with something like:
Equipment:
2 picks - picks are too important to lose one miner to an accident, and having two miners greatly speeds things up
1 or 2 axes - for woodcutting. I consider using wooden axes to cut wood an exploit
Metalworking gear:
1 anvil
10 bituminous coal. This will get you 80 fuel, which is more than enough to jumpstart metalworking. In a pinch, the coal can be made into blocks, e.g. for breaching an aquifer, for which 40 blocks is generally enough.
10 malachite or copper nuggets and 10 cassetirite. This will yield 80 bronze using only 10 fuel which is enough to make some good arms and armour for early military
1 charcoal. This is useful so you can immediately start using the coal without needing a wood furnace first
Cloth stuff:
some thread and cloth, for emergency healthcare. I've never actually used them but they're fairly cheap.
5 or so bags. I like quarry bushes and bags are needed for processing them.
Food:
Whatever is default, it has always lasted me long enough to get my farming set up.
Animals:
1+1 cat, for vermin hunting and sentries/bait
1+5 of some species of fowl. Apparently turkeys are best food wise, but I like peafowl for their blue feathers
Sometimes, 1+2 swine
Rarely, 1+2 sheep or goats
Dwarfs:
2 axedwarfs, 5 axe, 2 teach, 1 each armor, shield, dodge. One of them generally helps mining as well.
1 miner. You really want a full time miner.
1 farmer. As said above, you really want a farmer that is good at its job asap, as that will make the whole food industry more efficient.
1 mason. My mason is often busy around the clock making doors, cabinets, coffers, etc.
1 mixed noble - diagnoser, appraiser, judge of intent, consoler, pacifier
1 carpenter + stone crafter. You need both: carpenters make beds, wheelbarrows, and bins, and stone crafters make rock pots and rock crafts, which are often my first export product. However, you don't really need them full time, and we don't have eight dwarfs.
I generally only give dwarfs one skill max. They pick up other jobs (cooking, distilling, etc) as needed, but as soon as possible these are taken over by a migrant so the dwarf can specialize in one job. If I have points left I can give some points, but I think these are better spent bringing more coal, cassetirite, or lumber.
I leave out all the wooden stuff, that can be made quite easily. If the embark has a lack of trees, it can pay to bring some lumber as well.